The paper investigates the wave propagation characteristics of periodic two dimensional, auxetic lattice structures. Periodic structures in general feature unique wave propagation characteristics, whereby waves are allowed to propagate only within specific frequency bands. Two dimensional periodic structures complement this feature with a low frequency directional behavior. The combination of these unique characteristics makes two dimensional periodic structures ideal candidates for the design of pass-band directional mechanical filters. Focus is here placed on honeycomb lattice configurations. A sensitivity analysis is first presented to investigate the influence of band-gap and directional behaviors with respect to changes in the internal angle. The presented results demonstrate how re-entrant topologies feature enhanced wave attenuation capabilities with respect to hexagonal lay-outs. An optimization problem is then formulated by considering the internal angle as a design variable, and the width of the attenuation frequency ranges and angular range of propagation at low frequencies as objective functions. The identified optimal configurations feature combined properties which demonstrate the effectiveness of the analysis procedure.